How to use this course
Guglielmo Marconi did not discover radio waves, and he was not the only person to send signals with them. James Clerk Maxwell predicted the waves, Heinrich Hertz produced and detected them, and Oliver Lodge, Alexander Popov, Jagadish Chandra Bose and others built receivers before or alongside him. Marconi’s contribution was to push range relentlessly, first by a grounded vertical antenna, then by tuning, power and scale, and to build a company that turned laboratory physics into a global service. His transatlantic signal of 1901 went farther than the physics of the day said it could, and the explanation led to the discovery of the ionosphere.
Marconi was also a public figure of Fascist Italy. He joined the National Fascist Party in 1923, presided over the regime’s Royal Academy of Italy, and backed the mobilization of science for its wars, including the conquest of Ethiopia. Lesson 12 treats that record factually, with sources.
- Circuit theory: RLC circuits, resonance, impedance.
- Electromagnetism: Maxwell’s equations, plane waves, the radiation of an oscillating dipole.
- Ordinary differential equations with constant coefficients.
- For Lessons 08–10, some acquaintance with plasmas and Fourier analysis helps.
Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. The lessons follow the problems Marconi faced in roughly the order he faced them: making waves, detecting them, launching them efficiently, separating stations, reaching beyond the horizon, and focusing energy into beams.
Timeline
| 1874 | Born 25 April in Bologna, second son of Giuseppe Marconi, a landowner, and Annie Jameson, of the Irish whiskey family. |
| 1894 | Reads of Hertz’s experiments after Hertz’s death; begins experiments at the family’s Villa Griffone, Pontecchio. Uses the laboratory and library of Augusto Righi at Bologna. |
| 1895 | A grounded, elevated antenna carries signals about 2 km, beyond a hill. |
| 1896 | Moves to London with his mother. 2 June: files British patent application No. 12039. Demonstrations for William Preece of the Post Office. |
| 1897 | 13 May: first wireless message over open sea, Flat Holm to Lavernock Point. Demonstrations at La Spezia for the Italian navy. July: founds the Wireless Telegraph & Signal Company. |
| 1899 | 27 March: signals across the English Channel, Wimereux to South Foreland. |
| 1900 | Company renamed Marconi’s Wireless Telegraph Company. 26 April: British patent No. 7777 on tuned telegraphy. |
| 1901 | 12 December: reports receiving the Morse letter S from Poldhu, Cornwall, at Signal Hill, Newfoundland. |
| 1902 | February: tests aboard SS Philadelphia reveal the daylight effect. Magnetic detector. December: messages from Glace Bay, Nova Scotia, to Poldhu. |
| 1905 | Marries Beatrice O’Brien. Patents a horizontal directional aerial. |
| 1907 | 17 October: regular commercial transatlantic service, Glace Bay to Clifden, Ireland. |
| 1909 | Nobel Prize in Physics, shared with Ferdinand Braun. |
| 1912 | The Titanic’s Marconi operators summon rescue by wireless. |
| 1914 | 30 December: appointed a senator of the Kingdom of Italy. Albert Medal. |
| 1915–18 | Military service in the army and navy; 1917 member of the Italian mission to the United States. |
| 1919 | Italian plenipotentiary delegate to the Paris Peace Conference. Buys the yacht Elettra. |
| 1922 | Lecture in New York anticipates radar. |
| 1923 | Joins the National Fascist Party. Short-wave trials between Poldhu and the Elettra. |
| 1926 | First beam station, linking England and Canada. |
| 1927 | First marriage annulled; marries Maria Cristina Bezzi-Scali. President of the National Research Council (CNR). |
| 1929 | Created hereditary marquis. |
| 1930 | 19 September: president of the Royal Academy of Italy, and ex officio member of the Fascist Grand Council. |
| 1931 | 12 February: inaugurates Vatican Radio for Pope Pius XI. |
| 1932 | Microwave experiments; microwave radiotelephone link between Vatican City and Castel Gandolfo. |
| 1934 | Microwave navigation beacon at Sestri Levante. |
| 1935 | Italy invades Ethiopia; the BBC bars him from broadcasting for political reasons. |
| 1937 | Dies 20 July in Rome of heart disease, aged 63. Radio stations worldwide fall silent for two minutes. |
Bologna, Bedford, Livorno, 1874–1894
Guglielmo Marconi was born on 25 April 1874 in the Palazzo Dall’Armi Marescalchi in Bologna. His father, Giuseppe Marconi, was a landowner with an estate, the Villa Griffone, at Pontecchio in the hills south-west of the city. His mother, Annie Jameson, was Irish, a granddaughter of John Jameson, founder of the whiskey distillery. Guglielmo grew up bilingual. Between the ages of about two and six he lived with his mother and elder brother Alfonso in Bedford, England.
He had almost no formal schooling. Private tutors taught him at Bologna and during winters in Florence and Livorno, where the family often stayed. In Livorno, when he was about 17, he had lessons from Vincenzo Rosa, a physics teacher at the local lycée, whom he later remembered with gratitude. He read widely in electricity, built batteries and electrical gadgets, and admired the American and British inventors of telegraphy and electric light.
At Bologna, Augusto Righi, professor of physics at the university and a leading experimenter on Hertzian waves, allowed the young man to attend lectures and to use the laboratory and the university library. Righi had built an improved spark oscillator, with the spark gap immersed in oil, that produced waves a few centimetres long. Marconi was never his formal student, but Righi’s papers and apparatus were his technical starting point.
The Villa Griffone experiments, 1894–1896
Hertz died on 1 January 1894, and the obituaries that followed described his demonstration of electromagnetic waves. Marconi, then 20, later said that reading about the waves gave him the idea of using them to signal without wires. In the summer of 1894 he built a storm alarm that rang a bell when lightning radiated a burst of waves. By December he could ring a bell across a room from a transmitter, and he showed it to his mother.
In 1895 he moved his experiments outdoors at the Villa Griffone. His decisive change was to connect one side of the spark gap to a metal plate raised on a pole and the other side to a plate buried in the ground, and to do the same at the receiver. The range jumped. In the late summer of 1895 a signal crossed about 2 km, beyond the Celestini hill behind the villa. According to the family story, an assistant on the far side fired a rifle to confirm reception. Lesson 06 explains why the grounded vertical antenna worked so much better than Hertz’s isolated dipoles.
Finding no backing for the invention in Italy, Marconi and his mother decided to try England, where the Jameson family had connections and where the world’s largest merchant fleet and navy might want ship-to-shore signalling. They left for London early in 1896.
London: patent and company, 1896–1899
On 2 June 1896 Marconi filed British patent application No. 12039, “Improvements in transmitting electrical impulses and signals, and in apparatus therefor”. It was granted in July 1897 and is often called the first patent for wireless telegraphy. Through a family introduction he met William Preece, engineer-in-chief of the General Post Office, who had experimented with induction telegraphy and saw at once the value of Marconi’s system. With Post Office support Marconi gave demonstrations in London and on Salisbury Plain, for officials of the army and navy, reaching several kilometres by March 1897.
On 13 May 1897 he sent the first wireless message over open sea, from the island of Flat Holm to Lavernock Point near Cardiff, across the Bristol Channel, about 5 km. That summer he demonstrated his system for the Italian navy at La Spezia, reaching about 19 km. In July 1897 the Wireless Telegraph & Signal Company was founded in London to exploit the patents; it became Marconi’s Wireless Telegraph Company in 1900. Marconi, at 23, held a majority of the shares.
Ranges grew steadily. On 27 March 1899 signals crossed the English Channel from Wimereux, near Boulogne, to the South Foreland lighthouse in Kent. Ships began to carry Marconi sets operated by company employees. The next problem was interference: two transmitters in range of one receiver jammed each other. Tuning, the subject of Lesson 07 and of patent No. 7777, was Marconi’s answer.
Spark oscillators and Hertzian waves
For the general reader. The first radio transmitters made waves with sparks. A capacitor charged to high voltage discharges across a gap; the current surges back and forth through the circuit a few dozen times, dying away quickly, and each surge radiates a little electromagnetic energy. A spark transmitter produces a train of damped waves, which is why the early radio spectrum was crowded and noisy.
- Solve the damped LC circuit and identify frequency, damping and quality factor.
- Compute the power radiated by an oscillating dipole.
- Understand why damped wave trains occupy a wide band of frequencies.
The damped LC circuit
A capacitor \(C\) charged to \(V_0\) discharges through an inductance \(L\) and a resistance \(R\) (which includes the spark and the radiation resistance). Kirchhoff’s law for the charge \(q\) is
\[ L\ddot q+R\dot q+\frac{q}{C}=0. \]If \(R<2\sqrt{L/C}\), the charge oscillates as
\[ q(t)=q_0\,e^{-\alpha t}\Big(\cos\omega t+\frac{\alpha}{\omega}\sin\omega t\Big),\qquad \alpha=\frac{R}{2L},\quad \omega=\sqrt{\omega_0^2-\alpha^2},\quad \omega_0=\frac{1}{\sqrt{LC}}. \]The quality factor is \(Q=\omega_0L/R\), and the amplitude falls by the factor \(e^{-\pi/Q}\) per cycle (logarithmic decrement \(\delta=\pi/Q\)).
This is the analysis William Thomson (Lord Kelvin) gave in 1853 for the discharge of a Leyden jar. Hertz’s 1887 oscillators had \(L\) and \(C\) so small that \(\omega/2\pi\) was in the hundreds of megahertz. Marconi moved to much larger capacitances and inductances, and to long antennas, to lower the frequency and increase the stored energy.
Radiation from an oscillating dipole
A dipole of moment \(p(t)=p_0\cos\omega t\), small compared with the wavelength \(\lambda=2\pi c/\omega\), radiates the time-averaged power
\[ \langle P\rangle=\frac{\mu_0\,p_0^2\,\omega^4}{12\pi c}. \]Equivalently, a short wire of length \(\ell\) carrying a uniform current of amplitude \(I_0\) radiates \(\langle P\rangle=\tfrac12 R_{\mathrm{rad}}I_0^2\) with \(R_{\mathrm{rad}}=80\pi^2(\ell/\lambda)^2\ \Omega\).
Derivation sketch. The far field of an accelerating dipole is \(E_\theta=\frac{\mu_0\ddot p\sin\theta}{4\pi r}\). The Poynting flux \(E_\theta^2/(\mu_0 c)\) integrated over a sphere, with \(\int\sin^2\theta\,d\Omega=8\pi/3\), gives \(P=\mu_0\ddot p^2/(6\pi c)\), and averaging \(\cos^2\) over a cycle gives the factor \(\tfrac12\). For the wire, \(\dot p=I\ell\), so \(p_0=I_0\ell/\omega\), and \(\mu_0 c=120\pi\ \Omega\) yields \(R_{\mathrm{rad}}\).
Bandwidth of a damped train
A wave train \(e^{-\alpha t}\cos\omega t\) for \(t\ge0\) has a Fourier spectrum whose power is a Lorentzian centred at \(\omega\) with full width at half maximum \(2\alpha=\omega_0/Q\). Strongly damped spark transmitters, with \(Q\) of order 10, occupied a band about a tenth of their carrier frequency. A receiver could not separate two such stations on nearby wavelengths.
Exercise 4.1A spark transmitter has \(C=20\) nF, \(L=50\ \mu\)H and total resistance \(R=5\ \Omega\). Find the frequency, the wavelength, \(Q\), and the number of cycles until the amplitude falls to 1% of its initial value.
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Exercise 4.2A wire 10 m long carries a uniform current of amplitude 10 A at a wavelength of 1 km. Find its radiation resistance and radiated power. Why are short antennas inefficient?
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Exercise 4.3Show that the stored energy of the oscillator decays as \(e^{-2\alpha t}\) and that \(Q=2\pi\times\)(energy stored)/(energy lost per cycle) for \(Q\gg1\).
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Detectors: coherer to diode
For the general reader. A radio wave arriving at a distant receiver carries very little energy, and it oscillates far too fast for a telegraph relay to follow. Early receivers needed a device that changed its state when radio waves arrived and then could be reset. The first was the coherer, a tube of metal filings. Later came magnetic detectors, crystal rectifiers and vacuum diodes, all of which convert a rapid oscillation into a steady current.
- Understand the coherer as a threshold switch.
- Show that a nonlinear element rectifies an oscillating signal.
- Compute the detected output of a square-law detector for a modulated wave.
The coherer
Édouard Branly found in 1890 that loose metal filings, normally a poor conductor, become a good conductor when an electrical oscillation passes near them. Oliver Lodge named the device the coherer in 1894 and added a tapper to shake the filings loose. Marconi made a sensitive version: a small glass tube, partly evacuated, holding a pinch of nickel and silver filings between two silver plugs. In a receiving circuit with a battery and relay, the arrival of a wave train lowered the coherer’s resistance from megohms to hundreds of ohms; the relay closed, a Morse printer recorded a mark, and a tapper struck the tube to restore it.
The coherer is a threshold device. It responds to the peak voltage, not to the energy, and it gives the same output for a weak and a strong signal above threshold. It was slow, erratic and sensitive to atmospheric noise. In 1902 Marconi patented a magnetic detector, in which a moving band of iron wire passed through coils; the radio-frequency field changed the magnetic hysteresis of the iron, producing clicks in a telephone receiver. It replaced the coherer in most of his company’s equipment. The 1901 transatlantic reception (Lesson 08) used a self-restoring coherer with a telephone earpiece; its origin is linked to Jagadish Chandra Bose’s work of 1899 on mercury-iron contacts.
Rectification
Let a device have current–voltage characteristic \(i(v)=a_1v+a_2v^2+\cdots\). For an input \(v(t)=V(t)\cos\omega t\) with a slowly varying amplitude \(V(t)\), the output averaged over a radio-frequency cycle is
\[ \bar\imath(t)=\tfrac12a_2V(t)^2+O(V^4). \]The linear term averages to zero; the quadratic term gives \(\cos^2\omega t=\tfrac12(1+\cos2\omega t)\), whose slow part follows the envelope. Every detector in the history of radio, from Branly’s filings to the semiconductor diode, works by some nonlinearity of this kind. John Ambrose Fleming, Marconi’s scientific adviser, invented the vacuum diode valve in 1904 for exactly this purpose.
Exercise 5.1An amplitude-modulated wave \(v=V_0(1+m\cos\Omega t)\cos\omega t\) with \(\Omega\ll\omega\) drives a square-law detector. Find the components of the detected output at \(\Omega\) and \(2\Omega\), and the ratio of their amplitudes.
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Exercise 5.2An ideal diode passes current only when \(v>0\): \(i=v/R\) for \(v>0\), 0 otherwise. For \(v=V\cos\omega t\), find the average current. How does this envelope detector differ from the square-law detector?
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The grounded vertical antenna
For the general reader. Marconi’s first breakthrough, in 1895, was to raise one terminal of his transmitter high in the air and bury the other in the ground. The Earth acts as a mirror, so a vertical wire above it behaves like a wire twice as long. Longer wires radiate long waves far more efficiently, and long waves bend around obstacles and follow the curve of the ground. Marconi found that doubling the height of his antennas roughly quadrupled his range.
- Use the method of images to analyse a monopole over a conducting plane.
- Compute radiation resistance for short and quarter-wave monopoles.
- Derive the empirical rule that range grows as the square of antenna height.
The image principle
Above a perfectly conducting plane, the tangential electric field must vanish at the surface. A vertical current element at height \(z\) is matched by an image element at \(-z\) carrying current in the same direction. So a vertical wire of height \(h\) fed against the ground produces, in the upper half-space, exactly the field of a dipole of length \(2h\) in free space. The power flows only into the upper half-space, so it is half that of the full dipole for the same current.
- Short monopole of height \(h\ll\lambda\), with current falling linearly to zero at the top: \(R_{\mathrm{rad}}=40\pi^2(h/\lambda)^2\ \Omega\approx395\,(h/\lambda)^2\ \Omega\).
- Short monopole with a capacitive top load that keeps the current uniform: \(R_{\mathrm{rad}}=160\pi^2(h/\lambda)^2\ \Omega\).
- Quarter-wave monopole (\(h=\lambda/4\)): \(R_{\mathrm{rad}}\approx36.5\ \Omega\), half the 73 Ω of a half-wave dipole.
Derivation of (1) and (2). A dipole of length \(\ell=2h\) with uniform current has \(R=80\pi^2(2h/\lambda)^2\). Halving the power gives (2). With a triangular current distribution the dipole moment is half as large, so the power is a quarter: \(R=20\pi^2(2h/\lambda)^2\) for the dipole, and half that, \(40\pi^2(h/\lambda)^2\), for the monopole. Top loading with a horizontal wire or “umbrella” therefore multiplies the radiated power by four, which is why Marconi’s large stations used fans and umbrellas of wire hung from masts.
Range and height
Marconi observed that the range of his early sets increased roughly as the square of the antenna height, a rule later called Marconi’s law. A simple model explains it. The field radiated at distance \(d\) by a short vertical antenna of effective height \(h_t\) carrying current \(I\) is proportional to \(h_tI/(\lambda d)\). A receiving antenna of effective height \(h_r\) develops a voltage \(E h_r\). So the received voltage is
\[ V_r\ \propto\ \frac{h_t\,h_r\,I}{\lambda\,d}. \]With \(h_t=h_r=h\) and a fixed detector threshold, the maximum range scales as \(d_{\max}\propto h^2\).
Exercise 6.1An antenna 50 m high works at a wavelength of 1000 m. Compare its radiation resistance with and without a top load, and the efficiency in each case if ground and wire losses total 10 Ω.
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Exercise 6.2Marconi’s range was 2 km with poles of 8 m. Using \(d_{\max}\propto h^2\), what range would 30 m poles give? Why did the rule fail at long distances?
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Exercise 6.3Show that the far field of a vertical monopole over perfect ground has its maximum along the ground and vanishes straight up.
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Syntony: tuned and coupled circuits
For the general reader. Two tuning forks of the same pitch respond to each other; one of a different pitch stays silent. Radio receivers work the same way. Patent No. 7777, the “four sevens” of 1900, protected Marconi’s arrangement of tuned circuits in both the transmitter and the receiver, so that several stations could share the air without jamming one another.
- Derive the resonance curve of a series RLC circuit and its bandwidth.
- Find the normal modes of two inductively coupled resonant circuits.
- Understand the trade-off between selectivity and stored energy.
Resonance
Driven by a voltage \(V_0\cos\omega t\), a series RLC circuit carries current of amplitude
\[ I(\omega)=\frac{V_0}{\sqrt{R^2+\big(\omega L-\frac{1}{\omega C}\big)^2}}. \]It peaks at \(\omega_0=1/\sqrt{LC}\), and for \(Q=\omega_0L/R\gg1\) the power falls to half its peak at \(\omega_0\pm\omega_0/2Q\), so the bandwidth is \(\Delta\omega=\omega_0/Q\).
A receiving circuit with high \(Q\) accepts a narrow band. But selectivity is only useful if the transmitter also emits a narrow band. A plain antenna with a spark gap in it radiates its energy in a few cycles: low \(Q\), broad band (Lesson 04). Ferdinand Braun, from 1898, separated the spark circuit from the antenna and coupled them by a transformer, so that a high-\(Q\) closed circuit stored energy and fed it gradually to the antenna. Lodge had patented syntonic tuning in 1897. Marconi’s 7777 patent combined tuned, coupled circuits at both ends, with the antenna and the closed circuit adjusted to the same frequency.
Coupled circuits
Two identical LC circuits coupled by a mutual inductance \(M=kL\) obey, without losses,
\[ L\ddot q_1+M\ddot q_2+\frac{q_1}{C}=0,\qquad L\ddot q_2+M\ddot q_1+\frac{q_2}{C}=0. \]The symmetric and antisymmetric combinations \(q_1\pm q_2\) oscillate independently at
\[ \omega_\pm=\frac{\omega_0}{\sqrt{1\pm k}}. \]Energy put into circuit 1 passes to circuit 2 and back with the beat period \(2\pi/|\omega_--\omega_+|\approx2\pi/(k\omega_0)\) for small \(k\).
Adding and subtracting the equations gives \((L\pm M)\ddot q_\pm+q_\pm/C=0\). A tightly coupled spark transmitter therefore radiates on two frequencies, a defect that was cured by loose coupling and later by quenched spark gaps, which stop the primary oscillation after the first transfer of energy.
Exercise 7.1A receiver tuned to 500 kHz has \(Q=50\). A second station transmits at 520 kHz with the same field strength. By what factor is its received power reduced relative to the wanted station?
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Exercise 7.2Two circuits each tuned to 1 MHz are coupled with \(k=0.1\). Find the two frequencies of the coupled system and the time for energy to transfer from the primary to the secondary.
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Across the Atlantic: the ionosphere
For the general reader. In 1901 most physicists expected radio waves to travel in straight lines, like light, so that the bulge of the Earth would block a signal between Europe and America. Marconi tried anyway. On 12 December 1901, at Signal Hill in Newfoundland, he reported hearing three faint clicks, the letter S, sent from Cornwall. The next year Arthur Kennelly and Oliver Heaviside proposed that a conducting layer high in the atmosphere reflects the waves. That layer, the ionosphere, was confirmed in the 1920s.
- Compute the geometric horizon and show why straight-line propagation fails over 3500 km.
- Derive the plasma frequency and the reflection condition for radio waves in an ionized layer.
- Explain the daylight effect and the use of the secant law.
The experiment
The transmitter at Poldhu, Cornwall, designed with Fleming, used a large alternator to charge a high-voltage spark circuit feeding a fan of wires; a storm had destroyed the original circular antenna array that autumn. At Signal Hill, St. John’s, Marconi flew a receiving wire from a kite and listened with a telephone earpiece. The reception, which only Marconi and his assistant George Kemp heard, has been questioned by later historians because atmospheric noise is strong at that time of day and wavelength. Two months later, aboard the liner SS Philadelphia, Marconi recorded readable messages from Poldhu on a Morse tape up to 2496 km away at night, but much shorter distances by day. This “daylight effect” was the first clear sign of the ionosphere.
Plasma frequency
A layer of free electrons of density \(N\) responds to an electromagnetic wave of frequency \(\omega\). Each electron obeys \(m\ddot{\mathbf x}=-e\mathbf E\), giving a current \(\mathbf J=-Ne\dot{\mathbf x}\) and an effective permittivity
\[ \varepsilon(\omega)=\varepsilon_0\Big(1-\frac{\omega_p^2}{\omega^2}\Big),\qquad \omega_p^2=\frac{Ne^2}{\varepsilon_0 m}. \]A wave at normal incidence is reflected where the local plasma frequency reaches the wave frequency. The highest frequency reflected vertically, the critical frequency, is \(f_c=f_p(N_{\max})\approx8.98\sqrt{N_{\max}}\) Hz, with \(N\) in m\(^{-3}\). At oblique incidence with angle \(\theta_i\) from the vertical (flat-layer approximation), the maximum reflected frequency is
\[ f_{\max}=f_c\sec\theta_i. \]Below \(\omega_p\) the refractive index \(n=\sqrt{1-\omega_p^2/\omega^2}\) is imaginary and the wave cannot propagate. The secant law follows from Snell’s law in a horizontally stratified medium: \(n\sin\theta=\sin\theta_i\) is constant, and the ray turns back where \(n=\sin\theta_i\), that is, where \(\omega_p^2=\omega^2\cos^2\theta_i\).
Collisions between electrons and neutral molecules in the lowest, daytime D region absorb energy from the wave. At night the D region largely disappears, absorption drops, and long-distance reception improves: the daylight effect. Edward Appleton measured the height of the reflecting layer directly in 1924, and Gregory Breit and Merle Tuve did so with radio pulses in 1925.
Exercise 8.1Poldhu and Signal Hill are about 3500 km apart along the Earth’s surface (\(R_\oplus=6371\) km). How high would an object at Signal Hill have to be to be visible in a straight line from sea level at Poldhu? How high would a mid-path mirror have to be?
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Exercise 8.2The daytime F2 layer has a peak electron density of \(10^{12}\) m\(^{-3}\). Find the critical frequency, and the maximum usable frequency for a path where the ray meets the layer at \(\theta_i=75^\circ\).
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Exercise 8.3Show that for \(\omega>\omega_p\) the group velocity of a wave in the plasma is \(v_g=c\sqrt{1-\omega_p^2/\omega^2}\) and that \(v_gv_\phi=c^2\).
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Short waves and beam arrays
For the general reader. For twenty years long-distance radio meant enormous stations on very long wavelengths, kilometres long. In the early 1920s Marconi, working from his yacht Elettra, showed that short waves, tens of metres long, could cross oceans with a fraction of the power, especially if many antennas were arranged in a row to send the energy in one direction like a searchlight. His beam system reshaped international communication.
- Compute the array factor of a uniform linear array.
- Relate directivity, gain and effective area.
- Use the Friis transmission equation to compare antenna systems.
Array factor
Let \(N\) identical elements be spaced \(s\) apart along a line, fed with equal amplitudes and a progressive phase \(\alpha\). In the direction making angle \(\theta\) with the line, the field is the single-element field times the array factor
\[ |AF(\theta)|=\left|\frac{\sin(N\psi/2)}{N\sin(\psi/2)}\right|,\qquad \psi=ks\cos\theta+\alpha,\quad k=\frac{2\pi}{\lambda}. \]Derivation. Element \(n\) contributes \(e^{in\psi}\) relative to element 0. Summing the geometric series gives \(\frac{e^{iN\psi}-1}{e^{i\psi}-1}=e^{i(N-1)\psi/2}\frac{\sin(N\psi/2)}{\sin(\psi/2)}\); dividing by \(N\) normalizes the peak to 1. With \(\alpha=0\) the main beam is broadside (\(\theta=90^\circ\)), and its first nulls fall where \(N\psi/2=\pm\pi\), so the beam width shrinks as \(1/(Ns)\).
Marconi’s beam stations used curtains of vertical wires, many wavelengths wide, backed by reflector curtains a quarter-wavelength behind. The reflector cancels radiation to the rear and roughly doubles the forward gain. The first commercial beam station, linking England and Canada, opened in 1926, and services to South Africa, India and Australia followed in 1927.
For transmitting and receiving antennas of gains \(G_t,G_r\), separated by \(d\) in free space,
\[ \frac{P_r}{P_t}=G_tG_r\Big(\frac{\lambda}{4\pi d}\Big)^2. \]An antenna of gain \(G\) has effective area \(A_e=G\lambda^2/4\pi\).
Exercise 9.1A broadside array of 16 elements spaced \(\lambda/2\) apart. Find the angular width between first nulls on either side of the main beam.
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Exercise 9.2A beam system has a gain of 100 (20 dBi) at each end. By what factor does it reduce the transmitter power needed, compared with isotropic antennas, for the same received power? Express in decibels.
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Microwaves and radar
For the general reader. In a 1922 lecture in New York, Marconi suggested that short radio waves reflected from distant objects could reveal ships in fog. In the 1930s he experimented with waves less than a metre long: a radiotelephone link between the Vatican and the papal residence at Castel Gandolfo in 1932, a navigation beacon for ships in 1934, and a demonstration of radar principles in Italy in 1935. Radar itself was developed independently in several countries during the 1930s.
- Derive the radar range equation and its fourth-power law.
- Relate pulse timing to range and Doppler shift to radial velocity.
- Estimate the radio horizon for line-of-sight microwave links.
A transmitter of power \(P_t\) and antenna gain \(G\) illuminates a target of radar cross-section \(\sigma\) at range \(R\). With the same antenna for reception, the received power is
\[ P_r=\frac{P_tG^2\lambda^2\sigma}{(4\pi)^3R^4}. \]Derivation. The power density at the target is \(P_tG/(4\pi R^2)\). The target intercepts and reradiates isotropically the power \(\sigma P_tG/(4\pi R^2)\), giving density \(\sigma P_tG/(4\pi R^2)^2\) back at the antenna, which collects it over \(A_e=G\lambda^2/4\pi\). The fourth power of \(R\) is the great difficulty of radar: doubling the range needs sixteen times the power.
Timing and Doppler
A pulse returns after \(\tau=2R/c\), so \(R=c\tau/2\). A target moving with radial velocity \(v_r\ll c\) shifts the returned frequency by \(f_D=2v_r/\lambda\), the factor 2 arising because the target both receives and re-emits a Doppler-shifted wave.
Line-of-sight links
Microwaves pass through the ionosphere, so they reach only to the horizon, extended slightly by atmospheric refraction. An antenna at height \(h\) sees to a distance \(d\approx\sqrt{2kR_\oplus h}\), where \(k\approx4/3\) accounts for the standard refraction. Marconi’s 1932 tests found reception somewhat beyond the optical horizon, an early observation of this effect.
Exercise 10.1A radar echo returns 0.4 ms after the pulse. How far away is the target? If the pulse lasts 1 \(\mu\)s, what is the range resolution?
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Exercise 10.2A ship approaches a 3 GHz radar at 10 m/s. Find the Doppler shift.
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Exercise 10.3Two microwave antennas, each on a hill 750 m above sea level, face each other across the sea. Estimate the maximum range of the link with and without refraction (\(R_\oplus=6371\) km).
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Empire of wireless, 1900–1922
After the transatlantic success, the Marconi Company built a network of coastal and long-distance stations. Regular commercial transatlantic service opened on 17 October 1907 between Glace Bay, Nova Scotia, and Clifden, Ireland. Company policy, which allowed Marconi operators to communicate only with other Marconi stations except in emergencies, drew sharp protest from rival companies and governments, and the international radiotelegraph conventions of 1906 and 1912 moved toward compulsory intercommunication.
On 16 March 1905 Marconi married the Hon. Beatrice O’Brien, daughter of the 14th Baron Inchiquin. They had four children, one of whom died in infancy. In 1909 he shared the Nobel Prize in Physics with Ferdinand Braun, in recognition of their contributions to the development of wireless telegraphy. In April 1912 the Titanic’s wireless operators, Marconi Company employees, called the Carpathia to the rescue, and the disaster led governments to require continuous wireless watches on passenger ships. In Britain, the same year brought the Marconi scandal, in which government ministers were accused of trading in shares of the American Marconi company while the British company was negotiating a state contract for imperial stations.
On 30 December 1914 King Victor Emmanuel III appointed him to the Italian Senate. When Italy entered the First World War in 1915 he was commissioned in the army, later transferring to the navy, and worked on military radio, including short-wave directional systems. In 1917 he was a member of the Italian government mission to the United States, and in 1919 he was one of Italy’s plenipotentiary delegates at the Paris Peace Conference. After the war he bought a steam yacht, renamed it Elettra, and fitted it as a floating laboratory, from which he ran the short-wave experiments of Lesson 09.
DiscussionThe 1943 decision of the United States Supreme Court in Marconi Wireless Telegraph Co. of America v. United States held key claims of Marconi’s American tuning patent invalid because of prior work, chiefly by John Stone Stone, with that of Oliver Lodge and Nikola Tesla also discussed. Compare this with the 1909 Nobel citation. What is the difference between inventing a principle and building the system that made it useful, and how should credit be shared?
Fascism, death and legacy, 1922–1937
The political record
Marconi joined the National Fascist Party in 1923, the year after Benito Mussolini came to power. Historians differ on his motives. Gabriele Falciasecca, a scholar of his political life, regards his commitment as sincere; the biographer Riccardo Chiaberge sees a calculated move by a businessman who needed the regime’s protection, and says he found no sentence of dissent in Marconi’s writings. In a speech Marconi claimed the honour of being the first fascist in radiotelegraphy, comparing his role with Mussolini’s in politics.
Under the regime he held the highest scientific offices in Italy. In 1927 he became president of the National Research Council (CNR). In his inaugural address of February 1929 he insisted on the council’s scientific purpose and autonomy, against Mussolini’s wish to make it an instrument of propaganda and control. He was created a hereditary marquis in 1929. On 19 September 1930 he was appointed president of the Royal Academy of Italy, founded by the regime, and the office made him a member of the Fascist Grand Council; he attended a single session. In 1933 he also became president of the Istituto della Enciclopedia Italiana (Treccani).
In May 1934, at Mussolini’s direction, he chaired a committee coordinating the CNR with the armed forces, and he supported mobilizing scientists for the regime’s wars and imperial conquests. After Italy invaded Ethiopia in October 1935, press reports expected him to assist the army’s communications, and the BBC barred him from its broadcasts for political reasons. In 2002 the historian Annalisa Capristo published documents showing that Jewish candidates for the Royal Academy were excluded throughout his presidency, years before the racial laws of 1938, and that their files were marked with the letter E, for ebreo. Chiaberge attributes this to conformity with Mussolini’s wishes; Falciasecca argues that Marconi held no antisemitic convictions. These findings have since affected public commemoration; in 2022 Cardiff Council reconsidered a planned sculpture marking the 1897 Bristol Channel transmission.
His second marriage also tied him to the Catholic establishment. His first marriage was annulled on 27 April 1927, and in June 1927 he married Maria Cristina Bezzi-Scali, a Roman countess; their daughter Elettra was born in 1930. For Pope Pius XI he built Vatican Radio, inaugurated on 12 February 1931.
Death
Marconi had suffered from heart disease for several years. He died in Rome on 20 July 1937, aged 63. After a state funeral, radio transmitters around the world fell silent for two minutes the following day. In a Senate speech in December 1937, Mussolini praised him as an early adherent of fascism. He was buried in Bologna, and in 1941 his remains were moved to a mausoleum at the Villa Griffone.
Legacy
- Technology: ship-to-shore and transoceanic radiotelegraphy, the grounded antenna, tuned circuits in commercial practice, the short-wave beam system and early microwave links. The Marconi Company remained a major British electronics firm for most of the twentieth century.
- Science: his transatlantic signal of 1901 forced the theory of the ionosphere, and the daylight effect was its first clue.
- Credit: his priority as an inventor is contested, by supporters of Popov, Lodge, Tesla, Bose and others. His role as the person who made radio a practical global system is not.
- Politics: his record as a senior public figure of the Fascist regime, including the exclusion of Jewish scholars from the Academy he led, is part of his biography and is now treated as such by historians and public institutions.
Final projectWrite a two-page technical history of the Poldhu–Signal Hill link. Estimate the wavelength and the antenna radiation resistance from Lessons 04 and 06, explain why the straight-line picture forbade reception, and explain using Lesson 08 what propagation mode could have carried the signal by day and by night.
Sources and further reading
Biography
- Guglielmo Marconi, Wikipedia (English), and Guglielmo Marconi, Wikipedia (Italian).
- Nobel Foundation, Guglielmo Marconi: Biographical.
- Marconi, Guglielmo, Dizionario Biografico degli Italiani, Treccani.
- M. Raboy, Marconi: The Man Who Networked the World, Oxford University Press, 2016.
- D. Marconi, My Father, Marconi, 1962.
- Worldcrunch, Marconi’s shame, on Falciasecca, Chiaberge and the political record.
- A. Capristo, L’espulsione degli ebrei dalle accademie italiane, Zamorani, 2002.
- Campaign Against Antisemitism, Cardiff Council reconsidering sculpture, 8 June 2022.
Physics and technology
- G. Marconi, Wireless telegraphic communication, Nobel lecture, 11 December 1909.
- G. Marconi, British patent No. 12039 (1896) and No. 7777 (1900).
- Marconi Wireless Telegraph Co. of America v. United States, 320 U.S. 1 (1943).
- J. A. Ratcliffe, Scientists’ reactions to Marconi’s transatlantic radio experiment, Proceedings of the IEE 121 (1974).
- H. G. J. Aitken, Syntony and Spark: The Origins of Radio, Princeton University Press, 1985.
- J. D. Jackson, Classical Electrodynamics, 3rd ed., Wiley, 1999, chapters 7 and 9.
- K. Davies, Ionospheric Radio, Peter Peregrinus, 1990.